arXiv subjects

Ashit Baran Aich

Publications and source records attributed to Ashit Baran Aich.

9 recordsLinked to original sources

arXiv2026

Temporal Conformal Prediction (TCP): Rolling Calibration for Financial Risk Forecasting

We study two rolling conformal procedures that construct prediction intervals for financial returns. Temporal Conformal Prediction (TCP) uses a zero-truncated version of the conformalized quantile regression (CQR) score. TCP-RM adds an offset updated from observed coverage errors with a decaying step size. We compare ten forecasting methods and two diagnostic controls across thirteen financial series on 1,448 common forecast dates. The nominal interval coverage is 95\%. TCP attains coverage of 95.23% for the S\&P 500, 95.37% for Bitcoin and 94.27% for Gold. Across all thirteen series, CQR has the smallest mean absolute deviation from the coverage target, followed by TCP and TCP-RM. TCP and CQR produce different intervals on 3.655% of forecasts. TCP-RM changes coverage and width little at the main settings. Coverage and interval score give different rankings. In 52 paired interval-score comparisons between TCP and four volatility-based benchmarks, 42 favour the volatility model and ten show no significant difference. These are individual Diebold--Mariano tests at the 5% level without a multiple-testing adjustment. Crisis-window results vary across markets, and good full-sample interval coverage does not ensure lower-tail calibration. The standard split-conformal guarantee requires exchangeability and does not automatically apply to the dependent returns evaluated here. The results support evaluating rolling conformal forecasts through coverage, interval scores and separate tail diagnostics, rather than closeness to the coverage target alone.

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arXiv2026

From Sublinear to Linear: Local Convergence in Finite-Width Networks via Locally Polyak-Lojasiewicz Regions

We study local linear convergence of gradient descent for finite-width feedforward networks under the squared empirical loss. Prior work shows that GD can remain confined to a Locally Quasi-Convex Region (LQCR) around initialization, but only gives a sublinear rate. We show that if the empirical Neural Tangent Kernel is positive at initialization, Lipschitz stable on the LQCR, and compatible with the LQCR radius, then the squared loss satisfies a local Polyak-Łojasiewicz inequality with constant $μ= λ_0 - L_Θr(\Rcal) > 0$. Combined with fixed-step iterate containment in the LQCR, imposed as a hypothesis in the linear-rate theorem, this yields linear convergence on the region. The LQCR supplies localization; fixed-step containment is imposed as a hypothesis in the linear-rate theorem; and the PL inequality comes from NTK conditioning under squared loss. The result is therefore a sufficient local condition, not a claim that this mechanism is necessary or unique for fast convergence. Empirically, we probe the theory through NTK spectral gap, parameter drift, empirical PL ratio, and suboptimality decay. On binary MNIST, the NTK remains positive, the PL ratio has a positive lower envelope, and the loss shows geometric decay on the stable regime. In a width ablation, the fixed-step width-$1024$ run leaves the local regime; reducing the step size lowers final drift from $1.870$ to $0.158$, restores the observed local-regime diagnostics, and yields the largest empirical PL-ratio lower envelope observed in the study. A CNN robustness check on a CIFAR-10 subset shows the PL-ratio envelope remains positive across three seeds, with a positive lower envelope across all three seeds on the stable regime.

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arXiv2026

The Minimax Lower Bound of Kernel Stein Discrepancy Estimation

Kernel Stein discrepancies (KSDs) have emerged as a powerful tool for quantifying goodness-of-fit over the last decade, featuring numerous successful applications. To the best of our knowledge, all existing KSD estimators with known rate achieve $\sqrt n$-convergence. In this work, we present two complementary results (with different proof strategies), establishing that the minimax lower bound of KSD estimation is $n^{-1/2}$ and settling the optimality of these estimators. Our first result focuses on KSD estimation on $\mathbb R^d$ with the Langevin-Stein operator; our explicit constant for the Gaussian kernel indicates that the difficulty of KSD estimation may increase exponentially with the dimensionality $d$. Our second result settles the minimax lower bound for KSD estimation on general domains.

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arXiv2026

Bayesian Inference for Joint Tail Risk in Paired Biomarkers via Archimedean Copulas with Restricted Jeffreys Priors

We propose a Bayesian copula-based framework to quantify clinically interpretable joint tail risks from paired continuous biomarkers. After converting each biomarker margin to rank-based pseudo-observations, we model dependence using one-parameter Archimedean copulas and focus on three probability-scale summaries at tail level $α$: the lower-tail joint risk $R_L(θ)=C_θ(α,α)$, the upper-tail joint risk $R_U(θ)=2α-1+C_θ(1-α,1-α)$, and the conditional lower-tail risk $R_C(θ)=R_L(θ)/α$. Uncertainty is quantified via a restricted Jeffreys prior on the copula parameter and grid-based posterior approximation, which induces an exact posterior for each tail-risk functional. In simulations from Clayton and Gumbel copulas across multiple dependence strengths, posterior credible intervals achieve near-nominal coverage for $R_L$, $R_U$, and $R_C$. We then analyze NHANES 2017--2018 fasting glucose (GLU) and HbA1c (GHB) ($n=2887$) at $α=0.05$, obtaining tight posterior credible intervals for both the dependence parameter and induced tail risks. The results reveal markedly elevated extremal co-movement relative to independence; under the Gumbel model, the posterior mean joint upper-tail risk is $R_U(α)=0.0286$, approximately $11.46\times$ the independence benchmark $α^2=0.0025$. Overall, the proposed approach provides a principled, dependence-aware method for reporting joint and conditional extremal-risk summaries with Bayesian uncertainty quantification in biomedical applications.

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arXiv2026

Bag of Coins: A Statistical Probe into Neural Confidence Structures

Modern neural networks often produce miscalibrated confidence scores and struggle to detect out-of-distribution (OOD) inputs, while most existing methods post-process outputs without testing internal consistency. We introduce the Bag-of-Coins (BoC) probe, a non-parametric diagnostic of logit coherence that compares softmax confidence $\hat p$ to an aggregate of pairwise Luce-style dominance probabilities $\bar q$, yielding a deterministic coherence score and a p-value-based structural score. Across ViT, ResNet, and RoBERTa with ID/OOD test sets, the coherence gap $Δ=\bar q-\hat p$ reveals clear ID/OOD separation for ViT (ID ${\sim}0.1$-$0.2$, OOD ${\sim}0.5$-$0.6$) but substantial overlap for ResNet and RoBERTa (both ${\sim}0$), indicating architecture-dependent uncertainty geometry. As a practical method, BoC improves calibration only when the base model is poorly calibrated (ViT: ECE $0.024$ vs.\ $0.180$) and underperforms standard calibrators (ECE ${\sim}0.005$), while for OOD detection it fails across architectures (AUROC $0.020$-$0.253$) compared to standard scores ($0.75$-$0.99$). We position BoC as a research diagnostic for interrogating how architectures encode uncertainty in logit geometry rather than a production calibration or OOD detection method.

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arXiv2026

Copula-Stein Discrepancy: A Generator-Based Stein Operator for Archimedean Dependence

Kernel Stein discrepancies (KSDs) are widely used for goodness-of-fit testing, but standard KSDs can be insensitive to higher-order dependence features such as tail dependence. We introduce the Copula-Stein Discrepancy (CSD), which defines a Stein operator directly on the copula density to target dependence geometry rather than the joint score. For Archimedean copulas, CSD admits a closed-form Stein kernel derived from the scalar generator. We prove that CSD metrizes weak convergence of copula distributions, admits an empirical estimator with minimax-optimal rate $O_P(n^{-1/2})$, and is sensitive to differences in tail dependence coefficients. We further extend the framework beyond Archimedean families to general copulas, including elliptical and vine constructions. Computationally, exact CSD kernel evaluation is linear in dimension, and a random-feature approximation reduces the quadratic $O(n^2)$ sample scaling to near-linear $\tilde{O}(n)$; experiments show near-nominal Type~I error, increasing power, and rapid concentration of the approximation toward the exact $\widehat{\mathrm{CSD}}_n^2$ as the number of features grows.

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arXiv2025

Copula Discrepancy: Benchmarking Dependence Structure

We study a simple statistic for benchmarking how well a sample preserves a known bivariate dependence structure. Given a target copula family (Clayton or Gumbel) and parameter $θ_P$, the Copula Discrepancy (CD) compares the target Kendall's tau $τ(θ_P)$ with the Kendall's tau implied by a parameter $\hatθ$ fitted to the sample within the target family, i.e., $|τ(θ_P)-τ(\hatθ)|$. We develop a moment-based version, prove consistency, asymptotic normality, and robustness results under i.i.d.\ sampling, and use an MLE-based version empirically for greater power against tail-structure misspecification. Building on this, we define two information-theoretic copula summaries, a copula KL divergence (CKL) and a copula entropy gap (CED), and establish basic consistency and central limit results for their plug-in estimators. In controlled experiments, CD reliably separates on-target and off-target copulas with matched Kendall's $τ$, provides a dependence-aware signal for tuning SGLD step sizes where Effective Sample Size favors overly aggressive (and biased) settings, and remains stably nonzero under deliberate tail-dependence mismatch where a naive $τ$-based diagnostic fails; CKL and CED offer a complementary Shannon-style view that echoes these findings. Timing benchmarks show that both CD variants incur only millisecond-level overhead over the tested range and exhibit near-linear empirical scaling in sample size, providing a lightweight, dependence-focused complement to quadratic-cost omnibus discrepancies such as the Kernel Stein Discrepancy (KSD).

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arXiv2025

Deep Copula Classifier: Theory, Consistency, and Empirical Evaluation

We present the Deep Copula Classifier (DCC), a class-conditional generative model that separates marginal estimation from dependence modeling using neural copula densities. DCC is interpretable, Bayes-consistent, and achieves excess-risk $O(n^{-r/(2r+d)})$ for $r$-smooth copulas. In a controlled two-class study with strong dependence ($|ρ|=0.995$), DCC learns Bayes-aligned decision regions. With oracle or pooled marginals, it nearly reaches the best possible performance (accuracy $\approx 0.971$; ROC-AUC $\approx 0.998$). As expected, per-class KDE marginals perform less well (accuracy $0.873$; ROC-AUC $0.957$; PR-AUC $0.966$). On the Pima Indians Diabetes dataset, calibrated DCC ($τ=1$) achieves accuracy $0.879$, ROC-AUC $0.936$, and PR-AUC $0.870$, outperforming Logistic Regression, SVM (RBF), and Naive Bayes, and matching Logistic Regression on the lowest Expected Calibration Error (ECE). Random Forest is also competitive (accuracy $0.892$; ROC-AUC $0.933$; PR-AUC $0.880$). Directly modeling feature dependence yields strong, well-calibrated performance with a clear probabilistic interpretation, making DCC a practical, theoretically grounded alternative to independence-based classifiers.

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arXiv2025

A2 Copula-Driven Spatial Bayesian Neural Network For Modeling Non-Gaussian Dependence: A Simulation Study

In this paper, we introduce the A2 Copula Spatial Bayesian Neural Network (A2-SBNN), a predictive spatial model designed to map coordinates to continuous fields while capturing both typical spatial patterns and extreme dependencies. By embedding the dual-tail novel Archimedean copula viz. A2 directly into the network's weight initialization, A2-SBNN naturally models complex spatial relationships, including rare co-movements in the data. The model is trained through a calibration-driven process combining Wasserstein loss, moment matching, and correlation penalties to refine predictions and manage uncertainty. Simulation results show that A2-SBNN consistently delivers high accuracy across a wide range of dependency strengths, offering a new, effective solution for spatial data modeling beyond traditional Gaussian-based approaches.

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